Understanding Circular Seating Arrangements

This question involves a classic circular seating arrangement puzzle. We have eight people: P, M, D, A, F, H, R, and B, sitting around a circle, all facing the center. To solve this, we need to carefully read each clue and build the arrangement step-by-step.

Step-by-Step Deduction of the Arrangement

Let's break down the clues provided in the problem:

1. Clue 1: R is fourth to the right of A.
2. Clue 2: A is third to the right of P.
3. Clue 3: M is second to the left of H.
4. Clue 4: H is second to the left of P.
5. Clue 5: D is third to the right of B.

Combining Clues to Build the Seating Plan

Let's start placing people based on the interconnected clues:

• From Clue 2, if we place P, then A is third to the right of P.
• From Clue 4, H is second to the left of P. So, we can place H relative to P.
• From Clue 3, M is second to the left of H. Now we can place M relative to H (and thus P).
• From Clue 1, R is fourth to the right of A. Since we have placed A, we can now place R.

Let's visualize this. Imagine the circle has 8 positions. If P is at position 1:

• A is 3 positions clockwise from P (right direction).
• H is 2 positions anti-clockwise from P (left direction).
• M is 2 positions anti-clockwise from H.
• R is 4 positions clockwise from A.

Placing P, A, H, M, and R leaves three spots for D, F, and B.

Placing the Remaining People (D, F, B)

We use Clue 5: D is third to the right of B. We have three remaining spots. We need to find two spots among these three such that one person is three positions clockwise from the other. The only way this works with three adjacent remaining spots is if B and D occupy two of them, and the third person (F) fills the last spot.

Let's determine the final arrangement based on these steps. Assuming we place P at a certain spot, we can deduce the positions of A, H, M, and R. Then, the remaining spots must fit B, D, and F according to the last clue.

Let's represent the positions relative to P:

• Start with P.
• A is 3rd right of P.
• H is 2nd left of P.
• M is 2nd left of H.
• R is 4th right of A.

Let's assume positions are numbered 1 to 8 clockwise. If P is at 1:

• A is at 1 + 3 = 4.
• H is at 1 - 2 = -1 (or 8 - 1 = 7). H is at 7.
• M is 2nd left of H (at 7). Left is anti-clockwise. M is at 7 - 2 = 5.
• R is 4th right of A (at 4). Right is clockwise. R is at 4 + 4 = 8.

So far, we have: P(1), A(4), H(7), M(5), R(8). The positions used are 1, 4, 5, 7, 8. The remaining positions are 2, 3, 6.

The remaining people are B, D, and F, to be placed at positions 2, 3, and 6. Clue 5 says D is third to the right of B. Let's check the remaining spots:

• If B is at 2, 3rd right is 2+3=5 (taken by M). No.
• If B is at 3, 3rd right is 3+3=6. This works! If B is at 3, D is at 6.
• If B is at 6, 3rd right is 6+3=9 (or 9-8=1, taken by P). No.

So, B must be at position 3 and D at position 6. The last remaining spot (position 2) must be F.

Final Seating Arrangement (Clockwise)

Based on our deduction (starting with P at 1): P(1), F(2), B(3), A(4), M(5), D(6), H(7), R(8).

Let's check all clues with this arrangement:

1. R is 4th right of A? From A(4), 1st right is M(5), 2nd is D(6), 3rd is H(7), 4th is R(8). Yes.
2. A is 3rd right of P? From P(1), 1st right is F(2), 2nd is B(3), 3rd is A(4). Yes.
3. M is 2nd left of H? From H(7), 1st left is D(6), 2nd left is M(5). Yes.
4. H is 2nd left of P? From P(1), 1st left is R(8), 2nd left is H(7). Yes.
5. D is 3rd right of B? From B(3), 1st right is A(4), 2nd is M(5), 3rd is D(6). Yes.

The arrangement is correct.

Identifying Immediate Neighbors of B

In the final arrangement P, F, B, A, M, D, H, R (clockwise), B is at position 3. The people immediately next to B are at position 2 and position 4.

• The person at position 2 is F.
• The person at position 4 is A.

So, the immediate neighbors of B are F and A.

Comparing with Options

The options are:

1. AP
2. MP
3. AF
4. FM

The immediate neighbors of B are A and F. Option 3 is AF.

Conclusion on Seating Arrangement Puzzle

By carefully following each clue and constructing the circular seating arrangement step-by-step, we determined the position of all eight people. The immediate neighbors of B were identified as F and A.

Revision Table: Circular Seating Key Terms

Additional Information: Solving Seating Arrangement Puzzles

Seating arrangement questions are common in reasoning sections of competitive exams. Here are some tips for solving them:

• Visualize: Draw a circle and mark the number of seats.
• Start with a Fixed Point: If possible, start with a person whose position is given relative to a fixed direction (though in circular arrangements facing the center, relative positions are key). Often, picking one person and placing them anywhere simplifies the problem as all other positions are relative to them.
• Use Definite Information First: Clues like "X is third to the right of Y" are more useful initially than "X is next to Y".
• Combine Clues: Look for connections between clues. People mentioned in multiple clues help link different parts of the arrangement.
• Handle 'Not' Clues: Statements like "X is not next to Y" are used to eliminate possibilities later.
• Check Your Final Arrangement: Once you think you have the arrangement, read through all the original clues and ensure your setup satisfies every condition.